Question

use logarithmic differentiation to find

y=x^(x+2)

Answer 1

\[\ln(y)=\ln(x^{x+2}) =>\ln(y)=(x+2)\ln(x)\]

Answer 2

take derivative of both sides

Answer 3

\[\frac{y'}{y}=(1+0)\ln(x)+(x+2)\frac{1}{x}\]

Answer 4

now multiply both sides by y

Answer 5

\[y'=y[\ln(x)+\frac{x+2}{x}]=x^{x+2}[\ln(x)+\frac{x+2}{x}] \]